arXiv subjects

Jiachang Xu

Publications and source records attributed to Jiachang Xu.

2 recordsLinked to original sources

arXiv2025

Faithful tropicalization and Skeleton of $\overline{M}_{0,n}$

We propose a comparison between the Berkovich skeleton of Berkovich analytification of $(\overline{\textsf{M}}_{0,n},{\overline{\textsf{M}}_{0,n} \setminus \textsf{M}_{0,n}})$ and faithful tropicalization of $\textsf{M}_{0,n}$ over a complete discrete valued field. In particular, we proved the two combinatorial structures are the same in terms of valuation in $\overline{\textsf{M}}^{\textsf{an}}_{0,n}$.

math.AG↗

arXiv2025

On the structure of the complement of skeleton

We study the higher dimensional geometry of Berkovich spaces using virtual open disks, which are given by fibration of relative dimension $1$. Inspired by birational geometry, we conjecture that the Berkovich skeleton is the complement of the union of all virtual open disks, and prove this conjecture for $\mathcal{X}$ admitting a strictly semistable model with semiample canonical class.

math.AG↗